147 research outputs found
Solid hulls and cores of weighted H-infinity-spaces
No full text[EN] We determine the solid hull and solid core of weighted Banach spaces H-upsilon(infinity) of analytic functions functions f such that upsilon vertical bar f vertical bar is bounded, both in the case of the holomorphic functions on the disc and on the whole complex plane, for a very general class of radial weights upsilon. Precise results are presented for concrete weights on the disc that could not be treated before. It is also shown that if H-upsilon(infinity) is solid, then the monomials are an (unconditional) basis of the closure of the polynomials in H-upsilon(infinity). As a consequence H-upsilon(infinity) does not coincide with its solid hull and core in the case of the disc. An example shows that this does not hold for weighted spaces of entire functions.The research of Bonet was partially supported by the project MTM2016-76647-P. The research of Taskinen was partially supported by the Vaisala Foundation of the Finnish Academy of Sciences and Letters.Bonet Solves, JA.; Lusky, W.; Taskinen, J. (2018). Solid hulls and cores of weighted H-infinity-spaces. Revista Matemática Complutense. 31(3):781-804. https://doi.org/10.1007/s13163-018-0265-6S781804313Anderson, J.M., Shields, A.L.: Coefficient multipliers of Bloch functions. Trans. Am. Math. Soc. 224, 255–265 (1976)Bennet, G., Stegenga, D.A., Timoney, R.M.: Coefficients of Bloch and Lipschitz functions. Ill. J. Math. 25, 520–531 (1981)Bierstedt, K.D., Bonet, J., Galbis, A.: Weighted spaces of holomorphic functions on bounded domains. Mich. Math. J. 40, 271–297 (1993)Bierstedt, K.D., Bonet, J., Taskinen, J.: Associated weights and spaces of holomorphic functions. Stud. Math. 127, 137–168 (1998)Blasco, O., Galbis, A.: On Taylor coefficients of entire functions integrable against exponential weights. Math. Nachr. 223, 5–21 (2001)Blasco, O., Pavlovic, M.: Coefficient multipliers on Banach spaces of analytic functions. Rev. Mat. Iberoam. 27, 415–447 (2011)Bonet, J., Taskinen, J.: Solid hulls of weighted Banach spaces of entire functions. Rev. Mat. Iberoam. 34, 593–608 (2018)Bonet, J., Taskinen, J.: Solid hulls of weighted Banach spaces of analytic functions on the unit disc with exponential weights. Ann. Acan. Sci. Fenn. Math. 43, 521–530 (2018)Constantin, O., Peláez, J.A.: Boundedness of the Bergman projection on L p -spaces with exponential weights. Bull. Sci. Math. 139(3), 245–268 (2015)Dostanić, M.R.: Multipliers in the space of analytic functions with exponential mean growth. Asymptot. Anal. 65(3–4), 191–201 (2009)Dostanić, M.-R.: Integration operators on Bergman spaces with exponential weight. Rev. Mat. Iberoam. 23(2), 421–436 (2007)Jevtić, M., Pavlović, M.: On the solid hull of the Hardy-Lorentz space. Publ. Inst. Math. (Beogr.) (N.S.) 85(99), 55–61 (2009)Jevtić, M., Vukotić, D., Arsenović, M.: Taylor Coefficients and Coefficient Multipliers of Hardy and Bergman-Type Spaces. RSME Springer Series, vol. 2. Springer, Berlin (2016)Lindenstrauss, J., Tzafriri, L.: Classical Banach Spaces I. Springer, Berlin (1977)Lusky, W.: On the Fourier series of unbounded harmonic functions. J. Lond. Math. Soc. 2(61), 568–580 (2000)Lusky, W.: On the isomorphism classes of weighted spaces of harmonic and holomorphic functions. Stud. Math. 175, 19–45 (2006)Pau, J., Peláez, J.A.: Volterra type operators on Bergman spaces with exponential weights. Contemp. Math. 561, 239–252. Topics in complex analysis and operator theory. American Mathematical Society, Providence (2012)Pavlović, M.: On harmonic conjugates with exponential mean growth. Czech. Math. J. 49, 733–742 (1999)Pavlović, M.: Function Classes on the Unit Disc: An Introduction. De Gruyter Studies in Mathematics, vol. 52, p. 449. De Gruyter, Berlin (2014)Peláez, J.A., Rättyä, J.: Weighted Bergman Spaces Induced by Rapidly Increasing Weights, vol. 227, no. 1066, pp. vi+124. American Mathematical Society (2014)Shields, A.L., Williams, D.L.: Bounded projections, duality and multipliers in spaces of analytic functions. Trans. Am. Math. Soc. 162, 287–302 (1971
Monomial basis in Korenblum type spaces of analytic functions
No full text[EN] It is shown that the monomials A = (z(n))(n=0)(infinity) are a Schauder basis of the Frechet spaces A(+)(-gamma), gamma >= 0, that consists of all the analytic functions f on the unit disc such that (1 - vertical bar z vertical bar)(mu)vertical bar f(z)vertical bar is bounded for all mu > gamma. Lusky proved that A is not a Schauder basis for the closure of the polynomials in weighted Banach spaces of analytic functions of type H-infinity. A sequence space representation of the Frechet space A(+)(-gamma) is presented. The case of (LB)-spaces A(-)(-gamma), gamma > 0, that are defined as unions of weighted Banach spaces is also studied.Research of the third author was partially supported by the Vaisala Foundation of the Finnish Academy of Sciences and Letters.Bonet Solves, JA.; Lusky, W.; Taskinen, J. (2018). Monomial basis in Korenblum type spaces of analytic functions. Proceedings of the American Mathematical Society. 146(12):5269-5278. https://doi.org/10.1090/proc/14195S526952781461
On boundedness and compactness of Toeplitz operators in weighted H-infinity-spaces
No full text[EN] We characterize the boundedness and compactness of Toeplitz operators T-a with radial symbols a in weighted H-infinity-spaces H(v)(infinity)on the open unit disc of the complex plane. The weights v are also assumed radial and to satisfy the condition (B) introduced by the second named author. The main technique uses Taylor coefficient multipliers, and the results are first proved for them. We formulate a related sufficient condition for the boundedness and compactness of Toeplitz operators in reflexive weighted Bergman spaces on the disc. We also construct a bounded harmonic symbol f such that T-f is not bounded in H-v(infinity) for any v satisfying mild assumptions. As a corollary, the Bergman projection is never bounded with respect to the corresponding weighted sup-norms. However, we also show that, for normal weights v, all Toeplitz operators with a trigonometric polynomial as the symbol are bounded on H-v(infinity) . (C) 2020 Elsevier Inc. All rights reserved.The research of Bonet was partially supported by the projects MTM2016-76647-P and GV Prometeo/2017/102 (Spain). The research of Taskinen was partially supported by a research grant from the Faculty of Science of the University of Helsinki.Bonet Solves, JA.; Lusky, W.; Taskinen, J. (2020). On boundedness and compactness of Toeplitz operators in weighted H-infinity-spaces. Journal of Functional Analysis. 278(10):1-26. https://doi.org/10.1016/j.jfa.2019.108456S12627810Bonet, J., Lusky, W., & Taskinen, J. (2018). Solid hulls and cores of weighted H ∞ -spaces. Revista Matemática Complutense, 31(3), 781-804. doi:10.1007/s13163-018-0265-6Bonet, J., Lusky, W., & Taskinen, J. (2019). Solid cores and solid hulls of weighted Bergman spaces. Banach Journal of Mathematical Analysis, 13(2), 468-485. doi:10.1215/17358787-2018-0049Constantin, O., & Peláez, J. Á. (2015). Boundedness of the Bergman projection on Lp-spaces with exponential weights. Bulletin des Sciences Mathématiques, 139(3), 245-268. doi:10.1016/j.bulsci.2014.08.012Dostanić, M. R. (2004). UNBOUNDEDNESS OF THE BERGMAN PROJECTIONS ON SPACES WITH EXPONENTIAL WEIGHTS. Proceedings of the Edinburgh Mathematical Society, 47(1), 111-117. doi:10.1017/s0013091501000190Engliš, M. (2008). Toeplitz operators and weighted Bergman kernels. Journal of Functional Analysis, 255(6), 1419-1457. doi:10.1016/j.jfa.2008.06.026Grudsky, S., & Vasilevski, N. (2001). Bergman-Toeplitz operators: Radial component influence. Integral Equations and Operator Theory, 40(1), 16-33. doi:10.1007/bf01202952Harutyunyan, A., & Lusky, W. (2010). On L1-subspaces of holomorphic functions. Studia Mathematica, 198(2), 157-175. doi:10.4064/sm198-2-4Luecking, D. H. (1987). Trace ideal criteria for Toeplitz operators. Journal of Functional Analysis, 73(2), 345-368. doi:10.1016/0022-1236(87)90072-3Luecking, D. H. (2007). Finite rank Toeplitz operators on the Bergman space. Proceedings of the American Mathematical Society, 136(05), 1717-1724. doi:10.1090/s0002-9939-07-09119-8Lusky, W. (1995). On Weighted Spaces of Harmonic and Holomorphic Functions. Journal of the London Mathematical Society, 51(2), 309-320. doi:10.1112/jlms/51.2.309Lusky, W. (2006). On the isomorphism classes of weighted spaces of harmonic and holomorphic functions. Studia Mathematica, 175(1), 19-45. doi:10.4064/sm175-1-2Lusky, W., & Taskinen, J. (2008). Bounded holomorphic projections for exponentially decreasing weights. Journal of Function Spaces and Applications, 6(1), 59-70. doi:10.1155/2008/217160Lusky, W., & Taskinen, J. (2011). Toeplitz operators on Bergman spaces and Hardy multipliers. Studia Mathematica, 204(2), 137-154. doi:10.4064/sm204-2-3Mannersalo, P. (2016). Toeplitz operators with locally integrable symbols on Bergman spaces of bounded simply connected domains. Complex Variables and Elliptic Equations, 61(6), 854-874. doi:10.1080/17476933.2015.1120293STROETHOFF, K. (1998). Compact Toeplitz operators on Bergman spaces. Mathematical Proceedings of the Cambridge Philosophical Society, 124(1), 151-160. doi:10.1017/s0305004197002375Taskinen, J., & Virtanen, J. (2010). Toeplitz operators on Bergman spaces with locally integrable symbols. Revista Matemática Iberoamericana, 693-706. doi:10.4171/rmi/614Zorboska, N. (2003). Toeplitz operators with BMO symbols and the Berezin transform. International Journal of Mathematics and Mathematical Sciences, 2003(46), 2929-2945. doi:10.1155/s016117120321203
Spectral gaps for the linear water-wave problem in a channel with thin structures
No full textPeer reviewe
Heat equation in a periodic domain with special initial data
No full textWe consider the initial-boundary value problem with the Neumann boundary condition for the classical linear heat equation in unbounded domains ohm & subne; Rd which are periodic in all directions of the Cartesian coordinate system. Generalizing the results of a previous paper by the authors, we apply Floquet transform methods to obtain results on the large time decay rates of the solution in the sup-norm. We observe that for a general, integrable initial data, the solution decays at the same rate t-d/2 as in the case of the Cauchy problem in the entire Euclidean space. We also consider special initial data with vanishing x-integral and obtain a faster decay rate. In the main results of the paper we pose for the initial data certain more detailed conditions, which are related to the lowest eigenvalue and eigenfunction of the model problem coming from the Floquet transform. Faster decay rates are obtained for such initial data. (c) 2025 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).Peer reviewe
Triglyceride-rich lipoprotein remnants, low-density lipoproteins, and risk of coronary heart disease: a UK Biobank study
No full textAIMS: The strength of the relationship of triglyceride-rich lipoproteins (TRL) with risk of coronary heart disease (CHD) compared with low-density lipoprotein (LDL) is yet to be resolved. METHODS AND RESULTS: Single-nucleotide polymorphisms (SNPs) associated with TRL/remnant cholesterol (TRL/remnant-C) and LDL cholesterol (LDL-C) were identified in the UK Biobank population. In a multivariable Mendelian randomization analysis, TRL/remnant-C was strongly and independently associated with CHD in a model adjusted for apolipoprotein B (apoB). Likewise, in a multivariable model, TRL/remnant-C and LDL-C also exhibited independent associations with CHD with odds ratios per 1 mmol/L higher cholesterol of 2.59 [95% confidence interval (CI): 1.99–3.36] and 1.37 [95% CI: 1.27–1.48], respectively. To examine the per-particle atherogenicity of TRL/remnants and LDL, SNPs were categorized into two clusters with differing effects on TRL/remnant-C and LDL-C. Cluster 1 contained SNPs in genes related to receptor-mediated lipoprotein removal that affected LDL-C more than TRL/remnant-C, whereas cluster 2 contained SNPs in genes related to lipolysis that had a much greater effect on TRL/remnant-C. The CHD odds ratio per standard deviation (Sd) higher apoB for cluster 2 (with the higher TRL/remnant to LDL ratio) was 1.76 (95% CI: 1.58–1.96), which was significantly greater than the CHD odds ratio per Sd higher apoB in cluster 1 [1.33 (95% CI: 1.26–1.40)]. A concordant result was obtained by using polygenic scores for each cluster to relate apoB to CHD risk.
CONCLUSION: Distinct SNP clusters appear to impact differentially on remnant particles and LDL. Our findings are consistent with TRL/remnants having a substantially greater atherogenicity per particle than LDL
Singularities at the contact point of two kissing Neumann balls
No full textWe investigate eigenfunctions of the Neumann Laplacian in a bounded domain Omega subset of Rd, where a cuspidal singularity is caused by a cavity consisting of two touching balls, or discs in the planar case. We prove that the eigenfunctions with all of their derivatives are bounded in (Omega)over bar, if the dimension d equals 2, but in dimension d >= 3 their gradients have a strong singularity O(vertical bar x ? O vertical bar(-alpha)), alpha is an element of (0,2 - root 2] at the point of tangency O. Our study is based on dimension reduction and other asymptotic procedures, as well as the Kondratiev theory applied to the limit differential equation in the punctured hyperplane Rd(-1) backslash O . We also discuss other shapes producing thinning gaps between touching cavities. (c) 2017 Elsevier Inc. All rights reserved.Peer reviewe
FLOQUET PROBLEM AND CENTER MANIFOLD REDUCTION FOR ORDINARY DIFFERENTIAL OPERATORS WITH PERIODIC COEFFICIENTS IN HILBERT SPACES
No full textA first order differential equation with a periodic operator coefficient acting in a pair of Hilbert spaces is considered. This setting models both elliptic equations with periodic coefficients in a cylinder and parabolic equations with time periodic coefficients. Our main results are a construction of a pointwise projector and a spectral splitting of the system into a finite-dimensional system of ordinary differential equations with constant coefficients and an infinite-dimensional part whose solutions have better properties in a certain sense. This complements the well-known asymptotic results for periodic hypoelliptic problems in cylinders and for elliptic problems in quasicylinders obtained by P. Kuchment and S. A. Nazarov, respectively. As an application, a center manifold reduction is presented for a class of nonlinear ordinary differential equations in Hilbert spaces with periodic coefficients. This result generalizes the known case with constant coefficients explored by A. Mielke.Peer reviewe
THE BAND-GAP STRUCTURE OF THE SPECTRUM IN A PERIODIC MEDIUM OF MASONRY TYPE
No full textWe consider the spectrum of a class of positive, second-order elliptic systems of partial differential equations defined in the plane R-2. The coefficients of the equation are assumed to have a special form, namely, they are doubly periodic and of high contrast. More precisely, the plane R-2 is decomposed into an infinite union of the translates of the rectangular periodicity cell Omega(0), and this in turn is divided into two components, on each of which the coefficients have different, constant values. Moreover, the second component of Omega(0) consist of a neighborhood of the boundary of the cell of the width h and thus has an area comparable to h, where h > 0 is a small parameter. Using the methods of asymptotic analysis we study the position of the spectral bands as h -> 0 and in particular show that the spectrum has at least a given, arbitrarily large number of gaps, provided h is small enough.Peer reviewe
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